Immerse planks in water, placing a weight on top of each plank to keep it submerged. Soak at least 4 hours or overnight. Meanwhile, mix dressing, 1/4 cup of the parsley and the lemon peel and juice until well blended. Remove 1/4 cup of the dressing mixture; set aside for later use. Pour remaining dressing mixture into large resealable plastic bag; add chicken. Seal bag; turn over several times to evenly coat chicken with the dressing mixture. Refrigerate at least 2 hours to marinate.